Girl can secure 1st & 3rd, boy can secure 2nd position in : 6 x 5 x 5 = 150 ways ; As :
1st position holder can be chosen in 6 ways (among 6 girls)
2nd position holder can be chosen in 5 ways (among 5 boys)
3rd position holder can be chosen in ( among 5 remaining girls)
The arrangement of first, second & third :
It is same : If Girl G1 gets first rank & Girl G2 gets third rank, is same as ; Girl G1 gets third rank & Girl G2 gets first rank. So, two are considered the same group. Hence, number of arrangements are 150 / 2 = 75 arrangements.
Since it says ''times'', you have to change the mixed numbers into fractions which will turn the equation into 10/3 x 13/5 which = 130/15. When you turn that into a mixed number, it changes into 8 10/15 or 8 2/3.
